Generalised Thermostatistics

Abstract:In this contribution, we develop the Maxwell generalized thermodynamical relations via the metric derivative model upon the mapping to a continuous fractal space. This study also introduces the total q-derivative expressions depending on two variables, to describe nonextensive statistical mechanics and also the α-total differentiation with conformable derivatives. Some results in the literature are re-obtained, such as the physical temperature defined by Sumiyoshi Abe.

Section: Emergence Of Rényi Entropy From S Q As Tsallis Entropymentioning

confidence: 99%

“…According to Reference [37], the role of scale translation would be studied in a systematic manner, since the procedure of estimating parameters is sensitive to the scale on which the experimental data are presented.…”

Section: Emergence Of Rényi Entropy From S Q As Tsallis Entropymentioning

confidence: 99%

Generalized Maxwell Relations in Thermodynamics with Metric Derivatives

Weberszpil

Chen

2017

“…The following definition of the φ-deformed exponential can be found in Naudts [3] (Chapter 10). He first defined the φ-deformed logarithm as:…”

Section: Deformed Exponentialsmentioning

confidence: 99%

“…We introduce these deformed functions as examples of the more general definition of the φ-deformed exponential given by Naudts [3] (Chapter 10). Until now, the φ-exponential has mainly been used in statistical mechanics to generalize the standard Boltzmann-Gibbs mechanics.…”

Section: Introductionmentioning

confidence: 99%

Deformed Exponentials and Applications to Finance

Trivellato

2013

“…Examples include generalized hyperbolic distributions, Meixner distributions, Weibull distributions and various power-law tail distributions (e.g., Zipf-Pareto, Lévy or Tsallis-type distributions). In particular, the statistics associated with power-law tails accounts for a rich class of phenomena observed in many real-world systems ranging from financial markets, physics and biology to geoscience (see, e.g., [1,2] and the citations therein).…”

Section: Introductionmentioning

confidence: 99%

On the Uniqueness Theorem for Pseudo-Additive Entropies

Jizba

Korbel

2017

Abstract:The aim of this paper is to show that the Tsallis-type (q-additive) entropic chain rule allows for a wider class of entropic functionals than previously thought. In particular, we point out that the ensuing entropy solutions (e.g., Tsallis entropy) can be determined uniquely only when one fixes the prescription for handling conditional entropies. By using the concept of Kolmogorov-Nagumo quasi-linear means, we prove this with the help of Darótzy's mapping theorem. Our point is further illustrated with a number of explicit examples. Other salient issues, such as connections of conditional entropies with the de Finetti-Kolmogorov theorem for escort distributions and with Landsberg's classification of non-extensive thermodynamic systems are also briefly discussed.